Generating symmetric graphs

Area of Science:

• Network science
• Graph theory
• Dynamical systems

Background:

• Symmetry in graph topology is vital for synchrony in networked dynamical systems.
• Real-world networks often exhibit extensive symmetries.
• Existing graph generation algorithms struggle to produce graphs with desired symmetry patterns.

Purpose of the Study:

• To present a novel algorithm for generating graphs with arbitrary symmetry patterns.
• To enable the creation of representative random graphs for testing network theories.
• To facilitate the study of synchrony in complex systems with controlled symmetries.

Main Methods:

• Development of a new graph generation algorithm.
• Integration of the algorithm with existing graph generators.
• Focus on achieving specific symmetry patterns in generated graphs.

Main Results:

• The algorithm successfully generates graphs with any desired symmetry pattern.
• The method can be combined with other algorithms to control graph properties like degree distribution.
• Generated graphs are suitable for testing hypotheses on large sets of random networks.

Conclusions:

• The new algorithm addresses a critical gap in graph generation for network science.
• It provides a powerful tool for researchers studying synchrony and network topology.
• Enables more accurate modeling and analysis of real-world networked systems.